| Autor: |
Ramesh, Amrutha Varshini, Mishkin, Aaron, Schmidt, Mark, Zhou, Yihan, Lavington, Jonathan Wilder, She, Jennifer |
| Rok vydání: |
2023 |
| Předmět: |
|
| Druh dokumentu: |
Working Paper |
| Popis: |
We consider minimizing a smooth function subject to a summation constraint over its variables. By exploiting a connection between the greedy 2-coordinate update for this problem and equality-constrained steepest descent in the 1-norm, we give a convergence rate for greedy selection under a proximal Polyak-Lojasiewicz assumption that is faster than random selection and independent of the problem dimension $n$. We then consider minimizing with both a summation constraint and bound constraints, as arises in the support vector machine dual problem. Existing greedy rules for this setting either guarantee trivial progress only or require $O(n^2)$ time to compute. We show that bound- and summation-constrained steepest descent in the L1-norm guarantees more progress per iteration than previous rules and can be computed in only $O(n \log n)$ time. |
| Databáze: |
arXiv |
| Externí odkaz: |
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